16 May / June 2014 1.2. Temperature Retention Models
For small molecules it has been observed that simultaneously modelling the gradient shape and temperature is a very effective approach to optimise the separation selectivity. This is true also for peptides and proteins. The relationship which is normally used for small molecules (Eqn. 4) was, however, found to be insuffi cient for proteins.
ln k = f + g / T (4)
where f and g are analyte and system specifi c constants and T the column temperature typically, but not necessarily, expressed in Kelvin.
As shown in the plots in Figure 1, when plotting retention factor versus temperature, small molecules such as ibuprofen and toluene exhibit a linear relationship where retention increases with increasing temperature. Proteins, however, do not exhibit the same linear behaviour. To accurately account for the retention of proteins it was necessary to add a second order term (Eqn. 5).
ln k = f + g / T + h / T2 (5)
A literature study showed that others had previously made the same observation [5-7]. The difference in behaviour can be explained by the fact that the structure of proteins changes when heated. At low temperature the protein is folded and many functional groups are hidden within the protein and cannot interact with the stationary phase. As the temperature is increased, the protein unfolds and more groups are exposed which can interact with the stationary phase and thereby the retention increases with increasing temperature. At high temperature the protein becomes completely unfolded and its retention behaviour now mimics that of a small molecule, i.e., the retention starts to decrease with increasing temperature (Figure 2). One could imagine that a molecule fl ips from one conformational form to another as the temperature changes and that this would result in multiple linear regions [11]. However, based on our experience and what we can fi nd in the literature proteins seem to display a gradual change in conformation and retention behaviour that can be nicely fi tted by a 2nd polynomial.
order 2. Experimental 1.3. Combined Solvent Strength and Temperature Models
In order to numerically fi t a model that accounts for the infl uence of both gradient shape and temperature, a bilinear combination of the relevant solvent strength model (Eqn. 1, 2 or 3) and the temperature model (Eqn. 5) was employed. Thus, combining Eqn. 1 and 5 resulted in the following model (Eqn. 6):
ln k = a10 + a01 x + a10 / T + a11 x / T + a20 / T2 (a00 + a01 x) + (a10 + a11 x) / T + (a20 + a21 x) / T2 (a00 + a10 / T + a20 / T2
+ a21 x / T2 =
) + (a01 + a11 / T + a21 / T2 ) x (6) =
RPC and IEC retention and peak width data was collected for six proprietary proteins with a molecular weight of approx. 25 kDa. For each separation mode, data was collected for six or nine different combinations of gradient slope and temperature in order to fi t the models. In addition, data was also collected for nine to 13 different linear and segmented gradients in order to validate the applicability of the fi tted models.
RPC data was collected using an Acquity H-class system, a BEH300 C4 100 x 2.1 mm 1.7 um column, a fl ow rate of 0.4 mL/min and mobile phases mixed from A and B solvents consisting of 0.1% TFA in water and 0.1% TFA in acetonitrile, respectively.
IEC data was collected using a Protein Pak High Res Q 100 x 4.6 mm 5 µm, a fl ow rate of 0.5 mL/min and mobile phases mixed from A and B solvents consisting of 5 mM bis-tris propane pH 8.6 and 25% acetonitrile without and with 400 mM NaCl.
Calculations were initially made in Excel and later using an alpha version of a commercial software ACD/LC simulator [9] which contained the modifi ed models. The latter had been modifi ed to allow incorporation of custom gradient models (e.g., Eqn. 3 for IEC) in combination with 2nd
Figure 1. Retention as function of temperature for a small molecule ibuprofen and three proprietary proteins with a molecular weight ranging from approx. 5 to 100 kDa.
order temperature models (Eqn. 5). ACD/LC Simulator is a commercially available software package that aids in the optimisation of chromatographic methods (gradient optimisation, additive
It should be noted that for fi xed values of solvent strength or temperature the model is consistent with Eqn. 1 or 5, respectively.
Figure 2. Potential explanation to the temperature dependent retention behaviour of proteins. An increasing temperature unfolds the protein and exposes more groups that can interact with the stationary phase. When completely unfolded, the retention decreases with increasing temperature as for small molecules.
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